The inhomogeneous evolution of subgraphs and cycles in complex networks

Subgraphs and cycles are often used to characterize the local properties of complex networks. Here we show that the subgraph structure of real networks is highly time dependent: as the network grows, the density of some subgraphs remains unchanged, while the density of others increase at a rate that is determined by the network's degree distribution and clustering properties. This inhomogeneous evolution process, supported by direct measurements on several real networks, leads to systematic shifts in the overall subgraph spectrum and to an inevitable overrepresentation of some subgraphs and cycles.Comment: 4 pages, 4 figures, submitted to Phys. Rev.

Flow of magnetic repelling grains in a two-dimensional silo

During a typical silo discharge, the material flow rate is determined by the contact forces between the grains. Here, we report an original study concerning the discharge of a two-dimensional silo filled with repelling magnetic grains. This non-contact interaction leads to a different dynamics from the one observed with conventional granular materials. We found that, although the flow rate dependence on the aperture size follows roughly the power-law with an exponent $3/2$ found in non-repulsive systems, the density and velocity profiles during the discharge are totally different. New phenomena must be taken into account. Despite the absence of contacts, clogging and intermittence were also observed for apertures smaller than a critical size determined by the effective radius of the repulsive grains.Comment: 6 pages, 8 figure

Multifractal properties of growing networks

We introduce a new family of models for growing networks. In these networks new edges are attached preferentially to vertices with higher number of connections, and new vertices are created by already existing ones, inheriting part of their parent's connections. We show that combination of these two features produces multifractal degree distributions, where degree is the number of connections of a vertex. An exact multifractal distribution is found for a nontrivial model of this class. The distribution tends to a power-law one, $\Pi (q) \sim q^{-\gamma}$, $\gamma =\sqrt{2}$ in the infinite network limit. Nevertheless, for finite networks's sizes, because of multifractality, attempts to interpret the distribution as a scale-free would result in an ambiguous value of the exponent $\gamma$.Comment: 7 pages epltex, 1 figur

Examples of signature (2,2) manifolds with commuting curvature operators

We exhibit Walker manifolds of signature (2,2) with various commutativity properties for the Ricci operator, the skew-symmetric curvature operator, and the Jacobi operator. If the Walker metric is a Riemannian extension of an underlying affine structure A, these properties are related to the Ricci tensor of A

Magnetostatic bias in multilayer microwires: theory and experiments

The hysteresis curves of multilayer microwires consisting of a soft magnetic nucleus, intermediate non-magnetic layers, and an external hard magnetic layer are investigated. The magnetostatic interaction between magnetic layers is proved to give rise to an antiferromagnetic-like coupling resulting in a magnetostatic bias in the hysteresis curves of the soft nucleus. This magnetostatic biasing effect is investigated in terms of the microwire geometry. The experimental results are interpreted considering an analytical model taking into account the magnetostatic interaction between the magnetic layers.Comment: 6 pages, 7 figure

On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density

We are concerned with the long time behaviour of solutions to the fractional porous medium equation with a variable spatial density. We prove that if the density decays slowly at infinity, then the solution approaches the Barenblatt-type solution of a proper singular fractional problem. If, on the contrary, the density decays rapidly at infinity, we show that the minimal solution multiplied by a suitable power of the time variable converges to the minimal solution of a certain fractional sublinear elliptic equation.Comment: To appear in DCDS-

3D sensors for the HL-LHC

In order to increase its discovery potential, the Large Hadron Collider (LHC) accelerator will be upgraded in the next decade. The high luminosity LHC (HL-LHC) period demands new sensor technologies to cope with increasing radiation fluences and particle rates. The ATLAS experiment will replace the entire inner tracking detector with a completely new silicon-only system. 3D pixel sensors are promising candidates for the innermost layers of the Pixel detector due to their excellent radiation hardness at low operation voltages and low power dissipation at moderate temperatures. Recent developments of 3D sensors for the HL-LHC are presented.Comment: 8 pages, 5 figures, International Workshops on Radiation Imaging Detectors 201

Variable stars in Local Group Galaxies - II. Sculptor dSph

We present the identification of 634 variable stars in the Milky Way dSph satellite Sculptor based on archival ground-based optical observations spanning $\sim$24 years and covering $\sim$ 2.5 deg$^2$. We employed the same methodologies as the "Homogeneous Photometry" series published by Stetson. In particular, we have identified and characterized one of the largest (536) RR Lyrae samples so far in a Milky Way dSph satellite. We have also detected four Anomalous Cepheids, 23 SX Phoenicis stars, five eclipsing binaries, three field variable stars, three peculiar variable stars located above the horizontal branch - near to the locus of BL Herculis - that we are unable to classify properly. Additionally we identify 37 Long Period Variables plus 23 probable variable stars, for which the current data do not allow us to determine the period. We report positions and finding charts for all the variable stars, and basic properties (period, amplitude, mean magnitude) and light curves for 574 of them. We discuss the properties of the RR Lyrae stars in the Bailey diagram, which supports the coexistence of subpopulations with different chemical compositions. We estimate the mean mass of Anomalous Cepheids ($\sim$1.5M$_{\odot}$) and SX Phoenicis stars ($\sim$1M$_{\odot}$). We discuss in detail the nature of the former. The connections between the properties of the different families of variable stars are discussed in the context of the star formation history of the Sculptor dSph galaxy.Comment: 22 pages, 17 figures, 13 tables. Accepted for publication on MNRA

A Photometric Study of the Outer Halo Globular Cluster NGC 5824

Multi-wavelength CCD photometry over 21 years has been used to produce deep color-magnitude diagrams together with light curves for the variables in the Galactic globular cluster NGC 5824. Twenty-one new cluster RR Lyrae stars are identified, bringing the total to 47, of which 42 have reliable periods determined for the first time. The color-magnitude diagram is matched using BaSTI isochrones with age of $13$~Gyr. and reddening is found to be $E(B-V) = 0.15 \pm0.02$; using the period-Wesenheit relation in two colors the distance modulus is $(m-M)_0=17.45 \pm 0.07$ corresponding to a distance of 30.9 Kpc. The observations show no signs of populations that are significantly younger than the $13$~Gyr stars. The width of the red giant branch does not allow for a spread in [Fe/H] greater than $\sigma = 0.05$ dex, and there is no photometric evidence for widened or parallel sequences. The $V, c_{UBI}$ pseudo-color magnitude diagram shows a bifurcation of the red giant branch that by analogy with other clusters is interpreted as being due to differing spectral signatures of the first (75\%) and second (25\%) generations of stars whose age difference is close enough that main sequence turnoffs in the color-magnitude diagram are unresolved. The cluster main sequence is visible against the background out to a radial distance of $\sim17$ arcmin. We conclude that NGC 5824 appears to be a classical Oosterhoff Type II globular cluster, without overt signs of being a remnant of a now-disrupted dwarf galaxy.Comment: 26 pages, 15 figures, 4 tables, accepted for publication in Astronomical Journa

Millimeter polarisation of the protoplanetary nebula OH 231.8+4.2: A follow-up study with CARMA

In order to investigate the characteristics and influence of the magnetic field in evolved stars, we performed a follow-up investigation of our previous submillimeter analysis of the proto-planetary nebula (PPN) OH 231.8+4.2 (Sabin et al. 2014), this time at 1.3mm with the CARMA facility in polarisation mode for the purpose of a multi-scale analysis. OH 231.8+4.2 was observed at ~2.5" resolution and we detected polarised emission above the 3-sigma threshold (with a mean polarisation fraction of 3.5 %). The polarisation map indicates an overall organised magnetic field within the nebula. The main finding in this paper is the presence of a structure mostly compatible with an ordered toroidal component that is aligned with the PPN's dark lane. We also present some alternative magnetic field configuration to explain the structure observed. These data complete our previous SMA submillimeter data for a better investigation and understanding of the magnetic field structure in OH 231.8+4.2.Comment: 7 pages, 5 figures, 2 tables. Accepted for publication in MNRA